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Symmetry analysis of a system of modified shallow-water equations. (English) Zbl 1470.76022

Summary: We revise the symmetry analysis of a modified system of one-dimensional shallow-water equations (MSWE) recently considered by T. Raja Sekhar and V. D. Sharma [Commun. Nonlinear Sci. Numer. Simul. 17, No. 2, 630–636 (2012; Zbl 1245.35097)]. Only a finite dimensional subalgebra of the maximal Lie invariance algebra of the MSWE, which in fact is infinite dimensional, was found in the aforementioned paper. The MSWE can be linearized using a hodograph transformation. An optimal list of inequivalent one-dimensional subalgebras of the maximal Lie invariance algebra is constructed and used for Lie reductions. Non-Lie solutions are found from solutions of the linearized MSWE.

MSC:

76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids
76M60 Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics

Citations:

Zbl 1245.35097

Software:

DESOLVII
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

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